■ 표본집단의 공분산을 계산하는 방법을 보여준다. ▶ 표본집단 공분산 계산하기 예제 (C#)
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decimal[] xArray = new decimal[] { 20, 30, 40, 50, 60, 70 }; decimal[] yArray = new decimal[] { 24, 32, 33, 84, 46, 40 }; decimal sampleCovariance = CalculateSampleCovariance(xArray, yArray); Console.WriteLine($"표본집단 공분산 : {sampleCovariance}"); |
▶ 표본집단 공분산 계산하기 (C#)
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#region 표본집단 공분산
■ 모집단 공분산을 계산하는 방법을 보여준다. ▶ 모집단 공분산 계산하기 예제 (C#)
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decimal[] xArray = new decimal[] { 20, 30, 40, 50, 60, 70 }; decimal[] yArray = new decimal[] { 24, 32, 33, 84, 46, 40 }; decimal populationCovariance = CalculatePopulationCovariance(xArray, yArray); Console.WriteLine($"모집단 공분산 : {populationCovariance}"); |
▶ 모집단 공분산 계산하기 (C#)
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#region 모집단 공분산 계산하기 - CalculatePopulationCovariance(xArray, yArray) /// <summary> /// 모집단 공분산 계산하기 /// </summary> /// <param name="xArray">X 배열</param> /// <param name="yArray">Y 배열</param> /// <returns>모집단 공분산</returns> public decimal CalculatePopulationCovariance(decimal[] xArray, decimal[] yArray) { if(xArray.Length != yArray.Length) { throw new ArgumentException("X 배열과 Y 배열의 길이가 같아야 합니다."); } decimal xAverage = xArray.Average(); decimal yAverage = yArray.Average(); return xArray.Zip(yArray, (x, y) => (x - xAverage) * (y - yAverage)).Average(); } #endregion |
■ 레이블이 지정된 평균 및 표준편차가 있는 히스토그램 차트를 만드는 방법을 보여준다. ▶ MainForm.cs
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using System; using System.Drawing; using System.Linq; using System.Windows.Forms; using ScottPlot; using ScottPlot.Plottable; using ScottPlot.Statistics; namespace TestProject { /// <summary> /// 메인 폼 /// </summary> public partial class MainForm : Form { //////////////////////////////////////////////////////////////////////////////////////////////////// Constructor ////////////////////////////////////////////////////////////////////////////////////////// Public #region 생성자 - MainForm() /// <summary> /// 생성자 /// </summary> public MainForm() { InitializeComponent(); Plot plot = new Plot(800, 600); Random random = new Random(0); double[] valueArray = DataGen.RandomNormal(random, pointCount : 1234, mean : 178.4, stdDev : 7.6); (double[] countArray, double[] binEdgeArray) = Common.Histogram(valueArray, min : 140, max : 220, binSize : 1); double[] leftEdgeArray = binEdgeArray.Take(binEdgeArray.Length - 1).ToArray(); BarPlot barPlot = plot.AddBar(values : countArray, positions : leftEdgeArray); barPlot.BorderLineWidth = 0; barPlot.FillColor = ColorTranslator.FromHtml("#9bc3eb"); double[] smoothEdgeArray = DataGen.Range(start : binEdgeArray.First(), stop : binEdgeArray.Last(), step : 0.1, includeStop : true); double[] smoothDensityArray = Common.ProbabilityDensity(valueArray, smoothEdgeArray, percent : true); ScatterPlot scatterPlot = plot.AddScatterLines ( xs : smoothEdgeArray, ys : smoothDensityArray, lineWidth : 2, label : "확률" ); scatterPlot.YAxisIndex = 1; plot.YAxis2.Ticks(true); BasicStats basicStats = new BasicStats(valueArray); plot.AddVerticalLine(basicStats.Mean, Color.Black, 2, LineStyle.Solid, "평균"); plot.AddVerticalLine(basicStats.Mean - basicStats.StDev, Color.Black, 2, LineStyle.Dash, "1 SD"); plot.AddVerticalLine(basicStats.Mean + basicStats.StDev, Color.Black, 2, LineStyle.Dash); plot.AddVerticalLine(basicStats.Mean - basicStats.StDev * 2, Color.Black, 2, LineStyle.Dot, "2 SD"); plot.AddVerticalLine(basicStats.Mean + basicStats.StDev * 2, Color.Black, 2, LineStyle.Dot); plot.AddVerticalLine(basicStats.Min, Color.Gray, 1, LineStyle.Dash, "최소/최대"); plot.AddVerticalLine(basicStats.Max, Color.Gray, 1, LineStyle.Dash); plot.Legend(location : Alignment.UpperRight); plot.Title("성인 남성 신장"); plot.XAxis.Label("신장(cm)"); plot.YAxis.Label("횟수(#)"); plot.YAxis2.Label("확률(%)"); plot.SetAxisLimits(yMin : 0); plot.SetAxisLimits(yMin : 0, yAxisIndex : 1); this.formsPlot.Reset(plot); this.formsPlot.Refresh(); } #endregion } } |
TestProject.zip
■ 평균, 중간, 표준 편차, 상관 계수, ANOVA를 계산하는 방법을 보여준다. ▶ Program.cs
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using System; using System.IO; using System.Collections.Generic; using System.Linq; using RDotNet; namespace TestProject { /// <summary> /// 프로그램 /// </summary> class Program { //////////////////////////////////////////////////////////////////////////////////////////////////// Method ////////////////////////////////////////////////////////////////////////////////////////// Static //////////////////////////////////////////////////////////////////////////////// Private #region 소스 값 배열 구하기 - GetSourceValueArray(count) /// <summary> /// 소스 값 배열 구하기 /// </summary> /// <param name="count">카운트</param> /// <returns>소스 값 배열</returns> private static double[] GetSourceValueArray(int count) { double[] valueArray = new double[count]; Random random = new Random(DateTime.Now.Millisecond); for(int i = 0; i < count; i++) { valueArray[i] = random.NextDouble() * 100; } return valueArray; } #endregion #region R 실행 가능 경로 추가하기 - AddRExecutablePath() /// <summary> /// R 실행 가능 경로 추가하기 /// </summary> private static void AddRExecutablePath() { string pathValue = Environment.GetEnvironmentVariable("Path"); string rExecutablePath = @"C:\Program Files\R\R-3.4.1\bin\x64;C:\Program Files\R\R-3.4.1\bin\i386"; Environment.SetEnvironmentVariable("Path", pathValue + Path.PathSeparator + rExecutablePath); } #endregion #region 숫자 벡터 설정하기 - SetNumericVector(rEngine, variableName, sourceArray) /// <summary> /// 숫자 벡터 설정하기 /// </summary> /// <param name="rEngine">R 엔진</param> /// <param name="variableName">변수명</param> /// <param name="sourceArray">소스 배열</param> private static void SetNumericVector(REngine rEngine, string variableName, double[] sourceArray) { NumericVector numericVector = new NumericVector(rEngine, sourceArray); rEngine.SetSymbol(variableName, numericVector); } #endregion #region 숫자 벡터 설정하기 - SetNumericVector(rEngine, variableName, sourceEnumerable) /// <summary> /// 숫자 벡터 설정하기 /// </summary> /// <param name="rEngine">R 엔진</param> /// <param name="variableName">변수명</param> /// <param name="sourceEnumerable">소스 열거형</param> private static void SetNumericVector(REngine rEngine, string variableName, IEnumerable<double> sourceEnumerable) { NumericVector numericVector = new NumericVector(rEngine, sourceEnumerable); rEngine.SetSymbol(variableName, numericVector); } #endregion #region 평균 값 구하기 - GetAverageValue(rEngine, variableName) /// <summary> /// 평균 값 구하기 /// </summary> /// <param name="rEngine">R 엔진</param> /// <param name="variableName">변수명</param> /// <returns>평균 값</returns> private static double GetAverageValue(REngine rEngine, string variableName) { double averageValue = rEngine.Evaluate(string.Format("mean({0})", variableName)).AsNumeric().First(); return averageValue; } #endregion #region 중간 값 구하기 - GetMedianValue(rEngine, variableName) /// <summary> /// 중간 값 구하기 /// </summary> /// <param name="rEngine">R 엔진</param> /// <param name="variableName">변수명</param> /// <returns>중간 값</returns> private static double GetMedianValue(REngine rEngine, string variableName) { double medianValue = rEngine.Evaluate(string.Format("median({0})", variableName)).AsNumeric().First(); return medianValue; } #endregion #region 표준 편차 값 구하기 - GetStandardDeviationValue(rEngine, variableName) /// <summary> /// 표준 편차 값 구하기 /// </summary> /// <param name="rEngine">R 엔진</param> /// <param name="variableName">변수명</param> /// <returns>표준 편차 값</returns> private static double GetStandardDeviationValue(REngine rEngine, string variableName) { double medianValue = rEngine.Evaluate(string.Format("sd({0})", variableName)).AsNumeric().First(); return medianValue; } #endregion #region 상관 계수 값 구하기 - GetCorrelationValue(rEngine, variableName1, variableName2) /// <summary> /// 상관 계수 값 구하기 /// </summary> /// <param name="rEngine">R 엔진</param> /// <param name="variableName1">변수명 1</param> /// <param name="variableName2">변수명 2</param> /// <returns>상관 계수 값</returns> private static double GetCorrelationValue(REngine rEngine, string variableName1, string variableName2) { double correlationValue = rEngine.Evaluate(string.Format("cor({0}, {1})", variableName1, variableName2)).AsNumeric().First(); return correlationValue; } #endregion #region ANOVA 값 구하기 - GetANOVAValue(rEngine, variableName1, variableName2) /// <summary> /// ANOVA 값 구하기 /// </summary> /// <param name="rEngine">R 엔진</param> /// <param name="variableName1">변수명 1</param> /// <param name="variableName2">변수명 2</param> /// <returns>상관 계수 값</returns> private static double GetANOVAValue(REngine rEngine, string variableName1, string variableName2) { GenericVector genericVector = rEngine.Evaluate(string.Format("t.test({0}, {1})", variableName1, variableName2)).AsList(); double pValue = genericVector["p.value"].AsNumeric().First(); return pValue; } #endregion #region 프로그램 실행하기 - Main() /// <summary> /// 프로그램 실행하기 /// </summary> private static void Main() { AddRExecutablePath(); // 소스 값 배열을 설정한다. double[] sourceValueArray1 = GetSourceValueArray(1000000); double[] sourceValueArray2 = GetSourceValueArray(1000000); using(REngine rEngine = REngine.CreateInstance("RDotNet")) { rEngine.Initialize(); SetNumericVector(rEngine, "value1", sourceValueArray1); SetNumericVector(rEngine, "value2", sourceValueArray2); // 평균 값을 계산한다. double averageValue = GetAverageValue(rEngine, "value1"); Console.WriteLine("평균 값 : " + averageValue.ToString()); // 중간 값을 계산한다. double medianValue = GetMedianValue(rEngine, "value1"); Console.WriteLine("중간 값 : " + medianValue.ToString()); // 표준 편차 값을 계산한다. double standardDeviationValue = GetStandardDeviationValue(rEngine, "value1"); Console.WriteLine("표준 편차 : " + standardDeviationValue.ToString()); // 상관 계수 값을 계산한다. double correlationValue = GetCorrelationValue(rEngine, "value1", "value2"); Console.WriteLine("상관 계수 : " + correlationValue.ToString()); // ANOVA 값을 계산한다. double pValue = GetANOVAValue(rEngine, "value1", "value2"); Console.WriteLine("ANOVA : " + pValue.ToString()); } } #endregion } } |
※ 상기 소스는 실행에 앞서 R 3.4.1 버전이
■ R과 NMATH 계산 시간을 비교하는 방법을 보여준다. ▶ MainForm.cs
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using System; using System.Diagnostics; using System.IO; using System.Linq; using System.Windows.Forms; using RDotNet; using CenterSpace.NMath.Core; using CenterSpace.NMath.Stats; namespace TestProject { /// <summary> /// 메인 폼 /// </summary> public partial class MainForm : Form { //////////////////////////////////////////////////////////////////////////////////////////////////// Field ////////////////////////////////////////////////////////////////////////////////////////// Private #region Field /// <summary> /// 소스 값 배열 1 /// </summary> private double[] sourceValueArray1; /// <summary> /// 소스 값 배열 2 /// </summary> private double[] sourceValueArray2; #endregion //////////////////////////////////////////////////////////////////////////////////////////////////// Constructor ////////////////////////////////////////////////////////////////////////////////////////// Public #region 생성자 - MainForm() /// <summary> /// 생성자 /// </summary> public MainForm() { InitializeComponent(); string pathValue = Environment.GetEnvironmentVariable("Path"); string rBinarayPath = @"C:\Program Files\R\R-3.4.1\bin\x64;C:\Program Files\R\R-3.4.1\bin\i386"; Environment.SetEnvironmentVariable("Path", pathValue + Path.PathSeparator + rBinarayPath); this.runButton.Click += runButton_Click; } #endregion //////////////////////////////////////////////////////////////////////////////////////////////////// Method ////////////////////////////////////////////////////////////////////////////////////////// Private //////////////////////////////////////////////////////////////////////////////// Event #region 실행 버튼 클릭시 처리하기 - runButton_Click(sender, e) /// <summary> /// 실행 버튼 클릭시 처리하기 /// </summary> /// <param name="sender">이벤트 발생자</param> /// <param name="e">이벤트 인자</param> private void runButton_Click(object sender, EventArgs e) { this.sourceValueArray1 = GetSourceValueArray(1000000); this.sourceValueArray2 = GetSourceValueArray(1000000); CacluateWithR(); CalculateWithNMATH(); } #endregion //////////////////////////////////////////////////////////////////////////////// Function #region 소스 값 배열 구하기 - GetSourceValueArray(count) /// <summary> /// 소스 값 배열 구하기 /// </summary> /// <param name="count">카운트</param> /// <returns>소스 값 배열</returns> private double[] GetSourceValueArray(int count) { double[] valueArray = new double[count]; Random random = new Random(DateTime.Now.Millisecond); for(int i = 0; i < count; i++) { valueArray[i] = random.NextDouble() * 100; } return valueArray; } #endregion #region 계산하기 (R) - CacluateWithR() /// <summary> /// 계산하기 (R) /// </summary> private void CacluateWithR() { Stopwatch stopWatch = new Stopwatch(); using(REngine rEngine = REngine.CreateInstance("RDotNet")) { rEngine.Initialize(); #region 데이터를 변환한다. stopWatch.Start(); //NumericVector numericVector1 = rEngine.CreateNumericVector(this.sourceValueArray1); //NumericVector numericVector2 = rEngine.CreateNumericVector(this.sourceValueArray2); NumericVector numericVector1 = new NumericVector(rEngine, this.sourceValueArray1); NumericVector numericVector2 = new NumericVector(rEngine, this.sourceValueArray2); stopWatch.Stop(); long dataConversionTime = stopWatch.ElapsedMilliseconds; #endregion rEngine.SetSymbol("group1", numericVector1); rEngine.SetSymbol("group2", numericVector2); #region 평균 값을 계산한다. stopWatch.Restart(); double averageValue = rEngine.Evaluate("mean(group1)").AsNumeric().First(); stopWatch.Stop(); long averageValueTime = stopWatch.ElapsedMilliseconds; #endregion #region 중간 값을 계산한다. stopWatch.Restart(); double medianValue = rEngine.Evaluate("median(group1)").AsNumeric().First(); stopWatch.Stop(); long medianValueTime = stopWatch.ElapsedMilliseconds; #endregion #region 표준 편차 값을 계산한다. stopWatch.Restart(); double standardDeviationValue = rEngine.Evaluate("sd(group1)").AsNumeric().First(); stopWatch.Stop(); long standardDeviationValueTime = stopWatch.ElapsedMilliseconds; #endregion #region 상관 계수 값을 계산한다. stopWatch.Restart(); double correlationValue = rEngine.Evaluate("cor(group1, group2)").AsNumeric().First(); stopWatch.Stop(); long correlationValueTime = stopWatch.ElapsedMilliseconds; #endregion #region ANOVA 값을 계산한다. stopWatch.Restart(); GenericVector genericVector = rEngine.Evaluate("t.test(group1, group2)").AsList(); double pValue = genericVector["p.value"].AsNumeric().First(); stopWatch.Stop(); long pValueTime = stopWatch.ElapsedMilliseconds; #endregion this.dataConversionTimeTextBox1.Text = dataConversionTime.ToString(); this.avergageValueTextBox1.Text = averageValue.ToString(); this.averageValueTimeTextBox1.Text = averageValueTime.ToString(); this.medianValueTextBox1.Text = medianValue.ToString(); this.medianValueTimeTextBox1.Text = medianValueTime.ToString(); this.standardDeviationValueTextBox1.Text = standardDeviationValue.ToString(); this.standardDeviationValueTimeTextBox1.Text = standardDeviationValueTime.ToString(); this.correlationValueTextBox1.Text = correlationValue.ToString(); this.correlationValueTimeTextBox1.Text = correlationValueTime.ToString(); this.anovaValueTextBox1.Text = pValue.ToString(); this.anovaValueTimeTextBox1.Text = pValueTime.ToString(); } } #endregion #region 계산하기 (NMATH) - CalculateWithNMATH() /// <summary> /// 계산하기 (NMATH) /// </summary> private void CalculateWithNMATH() { Stopwatch stopwatch = new Stopwatch(); #region 데이터를 변환한다. stopwatch.Start(); DoubleVector doubleVector1 = new DoubleVector(this.sourceValueArray1); DoubleVector doubleVector2 = new DoubleVector(this.sourceValueArray2); stopwatch.Stop(); long dataConversionTime = stopwatch.ElapsedMilliseconds; #endregion #region 평균 값을 계산한다. stopwatch.Restart(); double averageValue = NMathFunctions.Mean(doubleVector1); stopwatch.Stop(); long averageValueTime = stopwatch.ElapsedMilliseconds; #endregion #region 중간 값을 계산한다. stopwatch.Restart(); double medianValue = NMathFunctions.Median(doubleVector1); stopwatch.Stop(); long medianValueTime = stopwatch.ElapsedMilliseconds; #endregion #region 표준 편차 값을 계산한다. stopwatch.Restart(); double standardDeviationValue = StatsFunctions.StandardDeviation(doubleVector1); stopwatch.Stop(); long standardDeviationValueTime = stopwatch.ElapsedMilliseconds; #endregion #region 상관 계수 값을 계산한다. stopwatch.Restart(); double correlationValue = StatsFunctions.Correlation(doubleVector1, doubleVector2); stopwatch.Stop(); long correlationValueTime = stopwatch.ElapsedMilliseconds; #endregion #region ANOVA 값을 계산한다. stopwatch.Restart(); OneWayAnova oneWayAnova = new OneWayAnova(); oneWayAnova.SetData(new DoubleVector[] { doubleVector1, doubleVector2 }); double pValue = oneWayAnova.AnovaTable.FStatisticPValue; stopwatch.Stop(); long pValueTime = stopwatch.ElapsedMilliseconds; #endregion this.dataConversionTimeTextBox2.Text = dataConversionTime.ToString(); this.averageValueTextBox2.Text = averageValue.ToString(); this.averageValueTimeTextBox2.Text = averageValueTime.ToString(); this.medianValueTextBox2.Text = medianValue.ToString(); this.medianValueTimeTextBox2.Text = medianValueTime.ToString(); this.standardDeviationValueTextBox2.Text = standardDeviationValue.ToString(); this.standardDeviationValueTimeTextBox2.Text = standardDeviationValueTime.ToString(); this.correlationValueTextBox2.Text = correlationValue.ToString(); this.correlationValueTimeTextBox2.Text = correlationValueTime.ToString(); this.anovaValueTextBox.Text = pValue.ToString(); this.anovaValueTimeTextBox.Text = pValueTime.ToString(); } #endregion } } |
TestSolution.zip
■ sd 함수를 사용해 표준 편차를 구하는 방법을 보여준다. ▶ 예제 코드 (R)
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매출 = read.csv("data_win.csv") sd(매출$구매건수) [1] 14569.13 |
■ var 함수를 사용해 분산을 구하는 방법을 보여준다. ▶ 예제 코드 (R)
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매출 = read.csv("data_win.csv") var(매출$구매건수) [1] 212259426 |
■ mean 함수를 사용해 평균을 구하는 방법을 보여준다. ▶ 예제 코드 (R)
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매출 = read.csv("data_win.csv") mean(매출$구매건수) [1] 24552.9 |
■ 표준 편차를 구하는 방법을 보여준다. ▶ 예제 코드 (C#)
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using System; using System.Collections.Generic; #region 표준 편차 구하기 - GetStandardDeviation(valueList, average) /// <summary> /// 표준 편차 구하기 /// </summary> /// <param name="valueList">값 리스트</param> /// <param name="average">평균</param> /// <returns>표준 편차</returns> public static double GetStandardDeviation(List<double> valueList, double average) { double variance = 0d; foreach(double value in valueList) { variance += Math.Pow(value - average, 2); } return Math.Sqrt(variance / valueList.Count); } #endregion |
■ 분산을 구하는 방법을 보여준다. ▶ 예제 코드 (C#)
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using System; #region 분산 구하기 - GetVariance(valueArray, average) /// <summary> /// 분산 구하기 /// </summary> /// <param name="valueArray">값 배열</param> /// <param name="average">평균</param> /// <returns>분산</returns> public static double GetVariance(double[] valueArray, double average) { int valueCount = valueArray.Length; if(valueCount == 0) { return 0d; } double variance = 0d; try { for(int i = 0; i < valueCount; i++) { variance += Math.Pow(valueArray[i] - average, 2); } } catch(Exception) { throw; } return variance; } #endregion |
■ 표준 편차를 구하는 방법을 보여준다. ▶ 예제 코드 (C#)
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using System; #region 표준 편차 구하기 - GetStandardDeviation(valueArray, average) /// <summary> /// 표준 편차 구하기 /// </summary> /// <param name="valueArray">값 배열</param> /// <param name="average">평균</param> /// <returns>표준 편차</returns> public double GetStandardDeviation(double[] valueArray, double average) { int valueCount = valueArray.Length; if(valueCount == 0) { return 0d; } double standardDeviation = 0d; double variance = 0d; try { for(int i = 0; i < valueCount; i++) { variance += Math.Pow(valueArray[i] - average, 2); } standardDeviation = Math.Sqrt(SafeDivide(variance, valueCount)); } catch(Exception) { throw; } return standardDeviation; } #endregion #region 안전하게 나누기 - SafeDivide(value1, value2) /// <summary> /// 안전하게 나누기 /// </summary> /// <param name="value1">값 1</param> /// <param name="value2">값 2</param> /// <returns>나눈 값</returns> private double SafeDivide(double value1, double value2) { double result = 0d; try { if((value1 == 0) || (value2 == 0)) { return 0d; } result = value1 / value2; } catch { } return result; } #endregion |
■ 평균을 구하는 방법을 보여준다. ▶ 예제 코드 (C#)
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#region 평균 구하기 - GetAverage(summary, valueCount) /// <summary> /// 평균 구하기 /// </summary> /// <param name="summary">합계</param> /// <param name="valueCount">값 카운트</param> /// <returns>평균</returns> public static double GetAverage(double summary, int valueCount) { if(valueCount == 0d) { return 0d; } double average = summary / valueCount; return average; } #endregion |